1. Construct the two-dimensional reciprocal space of a specimen containing needle-shaped precipitates according to the following directions.
a. The sample has a primitive cubic crystal structure with a lattice constant, a = 0.4 nm. Sketch a two-dimensional reciprocal lattice for the structure.
b. The TEM foil is 50 nm thick. Sketch the intensity distribution about the reciprocal lattice points in this case. If necessary, use an enlarged diagram of one point in order to keep the scales in perspective.
c. The foil contains coherent needle-shaped precipitates which are 2 nm in diameter and 20 nm long along the family of directions. Assume the precipitates have the same crystal structure as the matrix. Sketch the intensity distribution about the reciprocal lattice points in this case.
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